Dear Doug,
Let me suggest the following itinerary:
Arrive Midway (hopefully! at 7pm). Rent car at Midway. Drive to
nearby hotel (it's not the classiest area; you'll be fine at the
nearest Holiday Inn). Drive to relatives in Indiana. Drive back to
Chicago and drop car at Union Station. Take train.

The traffic from Midway to Chicago can be horrendous, and there is no
point in driving north into Chicago at the peak of traffic just to
sleep and push off back south on next morning. Backtracking through
Chicago's rush hours is no joy. The traffic out of Chicago to Indiana
will also slow you down....Midway is already south of the city and on
the way to Indiana.